[GAP Forum] lack of big space

[Max Neunhoeffer]

Dear Mohammad j.mamaghani,

as Max Horn already pointed out most of the time you will see the
alternating or the symmetric group and indeed then GAP has problems
computing a stabiliser chain if you simply call Size(g) in the
following situation:

gap> s := SymmetricGroup(2187);
gap> x := PseudoRandom(s);
gap> y := PseudoRandom(s);
gap> g := Group(x,y);

(this is a similar example, although not with 2187-cycles)

However, you can very efficiently do

gap> IsNaturalSymmetricGroup(g);
true
gap> IsNaturalAlternatingGroup(g);
false

which costs nearly no time and memory (very efficient special methods
are used for these). If one of these returned true then the group
knows its size without a stabiliser chain.
Once both these calls return false it should be relatively safe to
call 

gap> Size(g);

since theoretical results imply that then your group is much smaller
than Sym(2187) and - after all - it acts "only" on 2187 points. Then
GAP should be able to compute a stabiliser chain readily.

Another possibility is to use the recog package, which does this
analysis automatically in its
  RecogniseGroup
function. Note however that this package currently only provides
Monte Carlo algorithms which might go wrong.

Cheers,
  Max

On Mon, Aug 16, 2010 at 08:19:32AM -0700, mohammad j.mamaghani wrote:
> I would like to calculate the order of a subgroup of symmetric group S_2187 generated by two cycles of length 2187=3^7 using GAP, but gap has not enough space and does not accept all the members of the cycles . Are there any ways to use GAP for this problem?best regards mamaghaniAllameh Tabatabaei university dept of maths and  statsTehran, Iran.
> 
> 
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Max Neunhoeffer              http://www-groups.mcs.st-and.ac.uk/~neunhoef/
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